Did you answer YES on form DS-230 that you wanted the SSN issued? If yes, the SSA should have assigned the SSN by now and can tell you what the number is, even if they haven't printed and mailed out the card yet. Visit the local SSA with her passport and birth certificate and ask them for her SS number. Also ask if they've mailed the SS card.
You can apply for the reentry permit without her SSN. I only brought up the SSN because if you know it, that makes it easier for them to look up her A-number when you're at the Infopass appointment. The A-number is more important for the reentry permit.